共查询到20条相似文献,搜索用时 15 毫秒
1.
G. Indulal 《Linear algebra and its applications》2009,430(1):106-1296
The D-eigenvalues {μ1,μ2,…,…,μp} of a graph G are the eigenvalues of its distance matrix D and form the D-spectrum of G denoted by specD(G). The greatest D-eigenvalue is called the D-spectral radius of G denoted by μ1. The D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. In this paper we obtain some lower bounds for μ1 and characterize those graphs for which these bounds are best possible. We also obtain an upperbound for ED(G) and determine those maximal D-energy graphs. 相似文献
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We give upper and lower bounds for the spectral radius of a nonnegative matrix using its row sums and characterize the equality cases if the matrix is irreducible. Then we apply these bounds to various matrices associated with a graph, including the adjacency matrix, the signless Laplacian matrix, the distance matrix, the distance signless Laplacian matrix, and the reciprocal distance matrix. Some known results in the literature are generalized and improved. 相似文献
3.
Oscar Rojo 《Linear algebra and its applications》2008,428(4):754-764
Let G=(V(G),E(G)) be a unicyclic simple undirected graph with largest vertex degree Δ. Let Cr be the unique cycle of G. The graph G-E(Cr) is a forest of r rooted trees T1,T2,…,Tr with root vertices v1,v2,…,vr, respectively. Let
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Yanqing Chen 《Linear algebra and its applications》2010,433(5):908-913
Let G be a simple connected graph with n vertices and m edges. Denote the degree of vertex vi by d(vi). The matrix Q(G)=D(G)+A(G) is called the signless Laplacian of G, where D(G)=diag(d(v1),d(v2),…,d(vn)) and A(G) denote the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively. Let q1(G) be the largest eigenvalue of Q(G). In this paper, we first present two sharp upper bounds for q1(G) involving the maximum degree and the minimum degree of the vertices of G and give a new proving method on another sharp upper bound for q1(G). Then we present three sharp lower bounds for q1(G) involving the maximum degree and the minimum degree of the vertices of G. Moreover, we determine all extremal graphs which attain these sharp bounds. 相似文献
6.
Kinkar Ch. Das 《Linear algebra and its applications》2007,427(1):55-69
We consider weighted graphs, where the edge weights are positive definite matrices. In this paper, we obtain two upper bounds on the spectral radius of the Laplacian matrix of weighted graphs and characterize graphs for which the bounds are attained. Moreover, we show that some known upper bounds on the Laplacian spectral radius of weighted and unweighted graphs can be deduced from our upper bounds. 相似文献
7.
Let be a simple connected graph with vertices and edges. The spectral radius of is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of which improves some known bounds: If , where is an integer, then The equality holds if and only if is a complete graph or , where is the graph obtained from by deleting some edge . 相似文献
8.
Ji-Ming Guo 《Linear algebra and its applications》2006,413(1):59-71
This paper investigates how the Laplacian spectral radius behaves when the graph is perturbed by adding or grafting edges. 相似文献
9.
Let G be a simple connected graph of order n with degree sequence d1,d2,…,dn in non-increasing order. The signless Laplacian spectral radius ρ(Q(G)) of G is the largest eigenvalue of its signless Laplacian matrix Q(G). In this paper, we give a sharp upper bound on the signless Laplacian spectral radius ρ(Q(G)) in terms of di, which improves and generalizes some known results. 相似文献
10.
Dongmei Zhu 《Linear algebra and its applications》2010,432(11):2764-2772
In this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalue λ(G):
11.
Huiqiu Lin 《Linear and Multilinear Algebra》2013,61(4):442-447
Let D(G) denote the distance matrix of a connected graph G. The largest eigenvalue of D(G) is called the distance spectral radius of a graph G, denoted by ?(G). In this article, we give sharp upper and lower bounds for the distance spectral radius and characterize those graphs for which these bounds are best possible. 相似文献
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Denote by D(G)=(di,j)n×n the distance matrix of a connected graph G with n vertices, where dij is equal to the distance between vertices vi and vj in G . The least eigenvalue of D(G) is called the least distance eigenvalue of G , denoted by λn. In this paper, we determine all the graphs with λn∈[−2.383,0]. 相似文献
14.
F. Comellas 《Linear algebra and its applications》2007,423(1):74-80
In this paper we find spectral bounds (Laplacian matrix) for the vertex and the edge betweenness of a graph. We also relate the edge betweenness with the isoperimetric number and the edge forwarding and edge expansion indices of the graph allowing a new upper bound on its diameter. The results are of interest as they can be used in the study of communication properties of real networks, in particular for dynamical processes taking place on them (broadcasting, network synchronization, virus spreading, etc.). 相似文献
15.
On the spectral radius of trees with fixed diameter 总被引:2,自引:0,他引:2
Let T(n, d) be the set of trees on n vertices with diameter d. In this paper, the first spectral radii of trees in the set T(n, d) (3 ? d ? n − 4) are characterized. 相似文献
16.
Let G be a simple graph with least eigenvalue λ and let S be a set of vertices in G which induce a subgraph with mean degree k. We use a quadratic programming technique in conjunction with the main angles of G to establish an upper bound of the form |S|?inf{(k+t)qG(t):t>-λ} where qG is a rational function determined by the spectra of G and its complement. In the case k=0 we obtain improved bounds for the independence number of various benchmark graphs. 相似文献
17.
This paper studies the problem of estimating the spectral radius of trees with the given number of vertices and maximum degree. We obtain the new upper bounds on the spectral radius of the trees, and the results are the best upper bounds expressed by the number of vertices and maximum degree, at present. 相似文献
18.
Let GB(n,d) be the set of bipartite graphs with order n and diameter d. This paper characterizes the extremal graph with the maximal spectral radius in GB(n,d). Furthermore, the maximal spectral radius is a decreasing function on d. At last, bipartite graphs with the second largest spectral radius are determined. 相似文献
19.
Lingsheng Shi 《Linear algebra and its applications》2007,422(1):58-66
The spectral radius of a (directed) graph is the largest eigenvalue of adjacency matrix of the (directed) graph. We give the relation on the characteristic polynomials of a directed graph and its line graph, and obtain sharp bounds on the spectral radius of directed graphs. We also give the relation on the spectral radii of a graph and its line graph. As a consequence, the spectral radius of a connected graph does not exceed that of its line graph except that the graph is a path. 相似文献
20.
E. Gudiño 《Linear algebra and its applications》2010,433(1):233-240
We show that the spectral radius ρ(D) of a digraph D with n vertices and c2 closed walks of length 2 satisfies Moreover, equality occurs if and only if D is the symmetric digraph associated to a -regular graph, plus some arcs that do not belong to cycles. As an application of this result, we construct new sharp upper bounds for the low energy of a digraph, which extends Koolen and Moulton bounds of the energy to digraphs. 相似文献